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Final 1 - Honors Geometry
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Gravity
Key Concepts:
Terms in this set (77)
Point
specific location in a plane or space, can look like a dot(2D)
● No length or width
Line
straight, collection of points which go on infinitely in both directions(1D)
● Length but no width.
Plane
two dimensional surface which goes on infinitely in all directions(0D)
● Length and width
Collinear
two points on the same line
Coplanar
points on the same plane
Ray
portion of a line that has one endpoint and one side that continues forever
Opposite Rays
two rays that share the same endpoint and point in OPPOSITE
directions
Segment
Portion of a line with 2 endpoints
Unique Plane
3 noncollinear points
Unique Line
2 points
Skew Lines
set of lines of different planes, the two lines will never intersect
Parallel Lines
2 coplanar lines that do not intersect
Slop-Intercept form
y=mx+b
point slope form
y=m(x-x1)+y1
2 Parallel Lines
Same slope different y intercept
2 Perpendicular Lines
Opposite reciprocal slope
Distance Formula
d = √[( x₂ - x₁)² + (y₂ - y₁)²]
Midpoint formula
(x₁+x₂)/2, (y₁+y₂)/2
Segment Addition Postulate
If B is between A and C, then AB + BC = AC
complementary angles
2+ angles whose sum is 90 degrees
supplementary angles
2+ angles whose sum is 180 degrees
vertical angles
A pair of opposite congruent angles formed by intersecting lines
Linear Pair
Adjacent, supplementary angles
Adjacent Angles
Angles that have a common side and a common vertex
Acute Angle
an angle that measures less than 90 degrees
Obtuse Angle
An angle that measures more than 90 degrees but less than 180 degrees
Right Angle
an angle that measures 90 degrees
Straight Angles
measures exactly 180 degrees and forms a straight line
Reflex Angle
An angle greater than 180 degrees but less than 360
Interior Angles
angles inside a triangle
Triangle Sum Theorem
The sum of the measures of the interior angles of a triangle is 180 degrees
Exterior Angles
angles on the outside of triangle
Exterior Angles Theorem
The measure of an exterior angle of a triangle is equal to the sum of the measures of the two nonadjacent interior angles.
Transversal
a line that intersects two or more lines
Law of Detachment
If a conditional is true and its hypothesis is true, then its conclusion is true.
Law of Syllogism
If p-->q and q-->r are true statements, then p-->r is a true statement.
Statements
Conditional: If, then statement. Correlates to the contrapositive statement
Converse: A statement in which the if and then are switched
Inverse: A statement in which the if and then are negated but not switched
Contrapositive: A statement in which the if and then are both negated and
switched
Pairs (for statements)
Conditional/Contrapositive, Converse/Inverse
Biconditional Statement
"If and only if", all 4 statements are true
Corresponding Angles Postulate(CAP)
If two lines cut by a transversal, are parallel, then
corresponding angles are congruent.
Alternate Interior Angles Theorem(AIAT)
If two lines cut by a transversal are parallel, then
alternate interior angles are congruent.
Alternate Exterior Angles Theorem(AEAT)
If two parallel lines are cut by a
transversal the alternate exterior angles are congruent.
same side interior angles(SSIAT)
If two lines cut by a transversal are parallel, then the same-side interior angles
and supplementary.
Addition Property of Equality
If a=b, then a+c=b+c
Subtraction Property of Equality
If a=b, then a-c=b-c
Multiplication Property of Equality
If a=b, then ac=bc
Division Property of Equality
If a=b, then a/c=b/c
Reflexive Property of Equality
a=a
Symmetric Property of Equality
if a=b, then b=a
Transitive Property of Equality
If a=b and b=c, then a=c
substiution
if a=b, f(a)=f(b)
Similar
corresponding angle measurements are congruent, side lengths proportional, dilation, scale factor
Perimeter - Similarity
SF Sides=SF Sides
Area - Similarity
SF Sides = (SF Sides)^2
AA
2 angles, proves similar
SSS
3 sides, proves similar/congruent
SAS
2 sides, 1 angle inside, proves similar/congruent
ASA
2 angles, 1 side inside, proves congruent
AAS
2 angles, 1 side, proves congruent
Triangle Proportionality Theorem (Converse)
If a line parallel to one side of a triangle intersects the other two sides, then it divides the two sides proportionally.
Parallel Line Proportionality Theorem
If three parallel lines intersect two transversals, then they divide the transversals proportionally.
Bisector Proportionality Theorem
If a line bisects an angle, then it creates 2 new triangles with proportional sides
HL
1 hypotenuse, 1 leg of right triangle, proves congruent
CPCTC
corresponding parts of congruent triangles are congruent (angles, sides, parts, etc)
Equal Parts Theorem
If whole=part, other part is equal; if part=part, wholes =
Angle Bisector
a segment which bisects angle of triangle
Angle Bisector Theorem (converse)
if a point on the bisector of an angle, then it is equidistant from the sides of the angle
Incenter
the point where all three angle bisectors always intersect, inscribed in triangle, equidistant to triangle sides when measuring perpendicularly
Perpendicular Bisector
segment perpendicular to side of triangle and bisects side
Perpendicular bisector theorem (Converse)
If a point is on the perpendicular bisector of a segment, then it is equidistant from the endpoints of the segment.
Circumcenter
Point where all three perpendicular bisectors meet, center of circumscribed circle; acute-inside, right-on, obtuse-outside
Median
a segment from a vertex to the midpoint of the opposite side(through midpoint);cuts triangle in 2 equal areas
Centroid
point where all medians intersect, always inside triangle, long=2/3(whole)
Altitude (Height)
-A segment that goes from a vertex of the triangle and makes a 90° angle with the opposite side, known as the base
-Sometimes, the opposite side needs to be extended in order to accomplish this
Orthocenter
Point where all three altitudes intersect; acute-inside, right-on, obtuse-outside
Midsegment
segment that connects the midpoints of two sides of a triangle
Midsegment theorem
The segment connecting the midpoints of two sides of a triangle is parallel to the third side and is half as long as that side.
Midsegment parallel and half the length of base,
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